Question: Which of the following numbers is a factor of 135? ${7,9,12,13,14}$
Solution: By definition, a factor of a number will divide evenly into that number. We can start by dividing $135$ by each of our answer choices. $135 \div 7 = 19\text{ R }2$ $135 \div 9 = 15$ $135 \div 12 = 11\text{ R }3$ $135 \div 13 = 10\text{ R }5$ $135 \div 14 = 9\text{ R }9$ The only answer choice that divides into $135$ with no remainder is $9$ $ 15$ $9$ $135$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $9$ are contained within the prime factors of $135$ $135 = 3\times3\times3\times5 9 = 3\times3$ Therefore the only factor of $135$ out of our choices is $9$. We can say that $135$ is divisible by $9$.